Every equation of SARIMA I have found involves backshifts. I was wondering if I have an ARIMA model expressed like this: enter image description here

is it possible to express it in a similar way, without backshifts? Are there any resources where I can find seasonal ARIMA equation without backshifts?

  • $\begingroup$ Hi: There are ways to write ARIMA ( I'm not famiiar with SARIMA unless you just mean seasonal ) processes as state space models which would kind of avoid the use of the backshift operator but I'm not sure if that's what you're referring to. $\endgroup$ – mlofton Jan 19 at 17:38
  • $\begingroup$ I would like to express the SARIMA model similarly to how I have provided the equation for ARIMA. I have found some example for SARMA model here:docs.oracle.com/cd/E36352_01/epm.1112/cb_statistical/… Based on it how could I apply it to this formula: imgur.com/a/knlbmdA $\endgroup$ – domke89 Jan 19 at 17:41
  • $\begingroup$ Hi: apologies for my lack of understanding but your imgur link is just ARMA(p,q) so I don't know what you mean by your question. you can just add the two more summations if you want to make it an SARMA. $\endgroup$ – mlofton Jan 19 at 18:40
  • $\begingroup$ In the link that I have provided there's an equation for the SARMA model without backshifts. How would such an equation look for SARIMA? $\endgroup$ – domke89 Jan 19 at 19:52
  • $\begingroup$ Hi: I took another look to try and understand given what you said but the link doesn't seem to be showing anything any more ? $\endgroup$ – mlofton Jan 20 at 22:44

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